It is commonly believed that the energy bands of typical collinear antiferromagnets (AFs), which have zero net magnetization, are Kramers spin-degenerate. Kramers nondegeneracy is usually associated with a global time-reversal symmetry breaking (e.g., via ferromagnetism) or with a combination of spin–orbit interaction and broken spatial inversion symmetry. Recently, another type of spin splitting was demonstrated to emerge in some collinear magnets that are fully spin compensated by symmetry, nonrelativistic, and not even necessarily noncentrosymmetric. These materials feature nonzero spin density staggered in real space as seen in traditional AFs but also spin splitting in momentum space, generally seen only in ferromagnets. This results in a combination of materials characteristics typical of both ferromagnets and AFs. Here, we discuss this recently discovered class with application to a well-known semiconductor, FeSb2, and predict that with certain alloying, it becomes magnetic and metallic and features the aforementioned magnetic dualism. The calculated energy bands split antisymmetrically with respect to spin-degenerate nodal surfaces rather than nodal points, as in the case of spin–orbit splitting. The combination of a large (0.2-eV) spin splitting, compensated net magnetization with metallic ground state, and a specific magnetic easy axis generates a large anomalous Hall conductivity (∼150 S/cm) and a sizable magnetooptical Kerr effect, all deemed to be hallmarks of nonzero net magnetization. We identify a large contribution to the anomalous response originating from the spin–orbit interaction gapped anti-Kramers nodal surfaces, a mechanism distinct from the nodal lines and Weyl points in ferromagnets.
Dirac nodal lines protected against spin-orbit interaction in
IrO2
